Twitter help! How to contact someone?

[Rthrhr]

As I understood you can't send Direct Messages to people who aren't following you, but how do you then contact someone? Is it OK to ask someone to follow you, so that you can write him/her DM? And is it better to write him/her in reply or in mention? I asked someone to follow me in reply and I favorited the Tweet I replied to, but I can't see my reply showing, I only see that I favorited it.
Thanks in advance!

[Ashley Penilipe]

If you go on their page there will be a box where it says 'Tweet @ and whatever their name is, and if you type something they will get it even if they're not following you.